1

X-ray Scattering from Thin Films

Experimental methods for thin films analysis using X-ray scattering– Conventional XRD diffraction– Glancing angle X-ray diffraction– X-ray reflectivity measurement– Grazing incidence X-ray diffraction

X-ray diffraction study of real structure of thin films– Phase analysis– Residual stress analysis– Crystallite size and strain determination– Study of the preferred orientation– Study of the crystal anisotropy

2

Conventional X-ray diffraction

+ Reliable information on• the preferred orientation of crystallites• the crystallite size and lattice strain (in one

direction)

No information on the residual stress (constant direction of the diffraction vector)

Low scattering from the layer (large penetration depth)

Diffracting crystallites

3

Glancing angle X-ray diffraction GAXRD

0 20 40 60 80 100 120 140

10-2

10-1

100

=2/2

=20o

=10o

=5o

=2o

=1o

Pe

net

ratio

n d

epth

(m

)

Diffraction angle (o2)

Gold, CuK, 4000 cm-1

oi

oiexe

Idz

dIt

sinsin

sinsin;

1: 0

Symmetrical modeGAXRD

4

Other diffraction techniques used in the thin film analysis

Conventional diffraction with -

scanningqy=0

Grazing incidence X-ray diffraction

(GIXRD)qz0

Conventional diffraction with -

scanningqx=0

5

Penetration depth of X-rays

L.G. Parratt, Surface Studies of Solids by Total Reflection of X-rays, Physical Review 95 (1954) 359-369.

Example: Gold (CuK)

= 4.2558 10-5

= 4.5875 10-6

112

1

21

211

0

2

2

in

fiffr

n

rn

ee

e

0.0 0.5 1.0 1.5 2.0 2.5 3.0

10-3

10-2

10-1

100

Ref

lect

ivity

0.0 0.5 1.0 1.5 2.0 2.5 3.010

-4

10-3

10-2

10-1

TER

Pe

netr

atio

n d

ep

th (m

)

Glancing angle (o2)

222

;2

12

1

cos;coscos

ec

ce

cjjjV

rr

nnn

6

X-ray reflectivity measurement

0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,010

0

101

102

103

104

105

106

Inte

nsity

(a.

u.)

Diffraction angle (o2)

Si

Mo

Mo

Mo

t [Å] [Å]

0.68 19.6 5.8

0.93 236.5 34.0

1.09 14.1 2.71.00 5.0 2.7

1.00 2.8

Calculation of the electron density, thickness and interface roughness for each particular layer

W

The surface must be smooth (mirror-like)

Edge of TER

Kiessig oscillations (fringes)

7

Experimental set-up

Scintillationdetector

Flat monochromator

SampleGoebel mirror

X-ray source

Sample rotation,

Normal direction

Diffraction vector

Diffraction angle, 2

Angle of incidence,

Sample inclination,

Used for XRR, SAXS, GAXRD and symmetrical XRD

Information on the microstructure of thin films

Phase analysisResidual stress

analysisCrystallite size and

strain determinationStudy of the

preferred orientation

Study of the anisotropy in the lattice deformation

Investigation of the depth gradients of microstructure parameters

9

Uranium nitride – phase analysis

20 40 60 80 100 120 1400

200

400

600

800 GAXRD with = 3o

Radiation: Cu K

Inte

nsity

(cp

s)

Diffraction angle (o2)

20 30 40 50 60 70

101

102

103

222,

UN31

1, U

N

622

, U2N

3220,

UN

440

, U2N

3

Su

bst

rate

200,

UN

111,

UN

400

, U2N

3

222

, U2N

3

Inte

nsity

(cp

s)

Diffraction angle (o2)

Phase compositionPhase composition

1. UN, 80-90 mol.%Fm3m, a = 4.8897 Å

2. U2N3, 10-20% mol.%

Ia3, a = 10.64 10.68 Å

Sample depositionSample deposition

PVD in reactive atmosphere N2

Heated quartz substrate (300°C)

0 Atomic Percent Nitrogen 50 60 67

800

T(°C)

400

U UN U2N

3

UN

2

Schematic phase diagramSchematic phase diagram

10

U2N3 versus UN2

U

N

U2N3 (Ia3), a = 10.66 Å

U: 8b (¼, ¼, ¼)U: 24d (-0.018, 0, ¼)N: 48e (0.38, 1/6, 0.398)

UN2 (Fm3m)

a = 5.31 ÅU: 4a (0, 0, 0)N: 8c (¼, ¼, ¼)

Cannot be distinguished in thin

films

11

Uranium nitride – residual stress analysis

0.0 0.2 0.4 0.6 0.84.91

4.92

4.93

4.94

4.95

111

200

220

311

222

400

331

420

422

511

440

531

442

Lat

tice

pat

am

eter

(Å

)

sin2

UN

a0 = (4.926 ± 0.015) Å Compressive residual stress = (1.8 ± 0.8) GPa Strong anisotropy of lattice

deformation

U2N3

a0 = (10.636 ± 0.002) Å Compressive residual stress = (6.2 ± 0.1) GPa No anisotropy of lattice

deformation

GAXRD at =3°

0.00 0.04 0.08 0.12 0.16 0.2010.74

10.76

10.78

10.80

10.82

222

400

440

622

Latti

ce p

ara

met

er (

10-1

0 m)

sin2

12

Uranium nitride – anisotropic lattice deformation

111

2

02)coscossinsin(sin1

)(

2

)( dgphk

0.0 0.2 0.4 0.6 0.84.91

4.92

4.93

4.94

4.95

111

200

220

311

222

400

331

420

422

511

440

531

442

Lat

tice

pat

am

eter

(Å

)

sin2

0.00 0.05 0.10 0.15 0.2010.74

10.76

10.78

10.80

10.82

easy

hard

0.0 0.2 0.4 0.6 0.84.91

4.92

4.93

4.94

4.95

111

200

220

311

222

400

331

420

422

511

440

531

442

Measured Calculated

Lat

tice

pat

am

eter

(Å

)

sin2

UN a0 = (4.9270 ± 0.0015) Å = (1.0 ± 0.1) GPa

directions

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UN – anisotropic lattice deformation

0.0 0.1 0.2 0.3 0.4 0.5-1

0

1

2

3

4

5 422 511

Rel

ativ

e de

form

atio

n (1

0-3)

sin2

0.0 0.2 0.4 0.6 0.8 1.00.84

0.88

0.92

0.96

1.00

1.04

1.08

111

, 222

, 33

3

200

, 400

, 60

0

220

, 440

, 42

2

311

, 42

0

33

1

44

2

53

1

51

1

2 3/

1 =

2/(

1)

3 = 3(h2k2+k2l2+l2h2) / (h2+k2+l2)2

0.0 0.2 0.4 0.6 0.8-4

-2

0

2

4

6

440 531 442

Re

lativ

e d

efor

ma

tion

(10-3

)

sin2

Dependence of the lattice deformation on the

crystallographic direction

R.W. Vook and F. Witt, J. Appl. Phys., 36 (1965)

2169.

Related to the anisotropy of the elastic constants

14

UN versus U2N3

U

N

UN (Fm3m)

a = 4.93 ÅU: 4a (0, 0, 0)N: 4b (½, ½, ½)

Anisotropy of the mechanical

properties is related to the crystal

structure

U2N3 (Ia3), a = 10.66 Å

U: 8b (¼, ¼, ¼)U: 24d (-0.018, 0, ¼)N: 48e (0.38, 1/6, 0.398)

15

Methods for the size-strain analysis using XRD

Crystallite size

Fourier transformation of finite objects (with limited size)

Constant line broadening (with increasing diffraction vector)

Lattice strain

Local changes in the d-spacing Line broadening increases with

increasing q (a result of the Bragg equation in the differential form)

Scherrer Williamson-Hall Warren-Averbach Krivoglaz

P. Klimanek (Freiberg) R. Kuzel (Prague) P. Scardi (Trento) T. Ungar (Budapest)

(000) (100)

(001)

(011) (111)

(110)

(000) (100)

(001)

(011) (111)

(110)

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UN – anisotropic line broadening

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

111

200

220

31

122

2

400

331

42

0

422

511

/33

3

440

531

600

/44

2

D = 40 nm

e = 11x10-3

Lin

e br

oad

enin

g (

10-3 Å

-1)

sin

The Williamson-Hall plot

It recognises the anisotropy of the line broadening

It is robust (weak intensity, overlap of diffraction lines)

It is convenient if the higher-order lines are not available (nanocrystalline thin films, very thin films, GAXRD)

100

111

17

UN – texture measurement

Preferred orientation {110}

- 3 - 2 - 1 0 1

q (1/Å )

2

3

4

5

q (

1/Å

)z

x

111

200

220

311222

400

111200

220311222

-30 -20 -10 0 10 20 30

0

10

20

30

40

50

(220) (311)

Inte

gra

l int

ensi

ty (

a.u

.)

Sample inclination (deg)

0

sinsin2

;coscos2

y

ioziox

q

qq

Reciprocal space mapping

18

Reciprocal space mapping

Measured using CuK radiation-8 -7 -6 -5 -4 -3 -2 -1 0 1

0

1

2

3

4

5

6

7

8

9

1 1 1

-1 1 1

2 0 0

2 2 0

-2 2 0

3 1 1

3 -1 1

3 -1 -1

2 2 2

-2 2 2

4 0 0

3 3 1

-3 3 1

3 3 -1

4 2 0

4 -2 0

4 2 2

4 -2 2

4 -2 -2

3 3 3

5 1 1

5 -1 1

5 -1 -1

qx [1/A]

q z [1

/A]

{111}

-7 -6 -5 -4 -3 -2 -1 0 1

q(x), 1 /A

2

3

4

5

6

7

8

q(z

), 1

/A

111

222

220

311

4-22

33-1

420

331

422

A highly textured gold layer

19

Epitaxial growth of SrTiO3 on Al2O3

O in SrTiO3

a

b

cPowderCell 1.0

a

bcPowderCell 1.0

Sr

Al

Ti

O in Al2O3

q(x)

q(y)

100

200

300

400

500

600

700

800

900211

211

112

112

121

121

018

_118

_108

Reciprocal space map Atomic ordering in direct space

SrTiO3: Fm3m 111 axis -3 001 Al2O3: R-3c

20

SrTiO3 on Al2O3

Atomic Force Microscopy

Pyramidal crystallites with two different in-plane orientations

AFM micrograph courtesy of Dr. J. Lindner, Aixtron AG, Aachen.

111 111

_110

_110

21

TiCN

Depth resolved X-ray diffraction

122 123 124 125 126 127 128 129

30

45

60

75

90 = 10

o

= 8o

= 6o

= 4o

= 2o

Inte

nsi

ty (

a.u.

)

Diffraction angle (o2)

TiN

TiC

TiN

WC

t

t

dzz

dzzzp

p

0

0

sinsinsinsin

exp

sinsinsinsin

exp

Absorption of radiation

TiC TiN

22

Surface modification of thin films

Gradient of the residual stress in thin TiN coatings (CVD) implanted by metal ions: Y, Mo, W, Al and Cr

23

Functionally graded materials

W. Lengauer and K. Dreyer, J. Alloys Comp. 338 (2002) 194

SEM micrograph courtesy of C. Kral, Vienna University of Technology, Austria

Nitrogen – in-diffusion from N2

N-rich zone of (Ti,W)(C,N) Ti(C,N)

N-poor zone of (Ti,W)(C,N) (Ti,W)C

24

Study of concentration profiles

26.0 26.5 27.0 27.5 28.0

0

10

20

30

Diffraction angle (o2)

Inte

nsity

(cp

s)

0 2 4 6 8

4.30

4.28

4.26

4.24

~TiC0.75N0.25

TiN

Depth (m)

a (

Å)

122 124 126 128 130

0

5

10

15

20

Inte

nsi

ty (

cps)

Diffraction angle o2

0.0 0.5 1.0 1.54.27

4.26

4.25

4.24

~TiC0.3N0.7

TiN

Depth (m)

a (

Å)

Copper radiationPenetration depth: 1.8 m

Molybdenum radiationPenetration depth: 12.5 m

The lattice parameter must depend on concentration

25

SummaryBenefits of X-ray scattering

... for investigation of the real structure of thin films

Length scale between 10-2Å and 103Å is accessible (from atomic resolution to the layer thickness)

Small and variable penetration depth of X-ray into the solids (surface diffraction, study of the depth gradients)

Easy preparation of samples, non-destructive testing

Integral measurement (over the whole irradiated area)